External Beam Radiation Treatment (EBRT) for cancer involves irradiating an organ, tissue, or other region with ionizing radiation. EBRT changes the organ, tissue, or region and these changes may appear in magnetic resonance (MR) imagery of the treated organ, tissue, or region. Cancer treatment may be evaluated by detecting changes at the voxel-level in MR images of the treated organ, tissue, or region. Changes in pre-EBRT and post-EBRT images may be correlated with recurrence and complete or partial response to the EBRT. Quantifying the changes on a voxel-level involves spatially aligning, or registering, the pre-EBRT and post-EBRT MR images. However, little is known about specific changes to treated material as a function of EBRT. In one example, following EBRT, there is significant shrinkage and compression, as well as non-linear deformation, of the prostrate. Other treated regions may show other deformations. Registering pre-EBRT and post-EBRT MR images may be challenging due to the non-linear deformation, shrinkage or other changes, which may require using an elastic registration technique to achieve desired registration. Conventional registration methods employ simple linear registrations, including rigid registration, which may produce sub-optimal results. For example, inaccuracies in conventional registration of pre-EBRT and post-EBRT images may result in sub-optimal assessment of the changes to the treated area caused by the EBRT.
A Finite Element Model (FEM) in the context of EBRT and MR is a model that describes tissue properties including compressibility and elasticity. FEMs have traditionally been parameterized by a collection of finite elements such as tetrahedrons or hexahedrons connected at nodes. The material properties of elements define how a force at one node affects other nodes. FEMs have been employed to determine how a set of external forces displace tissue. Conventionally, FEMs have been employed to capture the motion of the various tissues on computed tomography (CT) imagery of cancer patients. Capturing this motion facilitates exploring different material properties for benign tissue, tumors, and benign afflictions such as prostatic hyperplasia. Chi et al., A material sensitivity study on the accuracy of deformable organ registration using linear biomechanical models, Med. Phys., vol. 33, no. 2, pp 421-433, February 2006. Similarly, FEMs model bladder, prostate, and rectum movement on CT imagery, with the results compared to a cadaver. Boubaker et al., Finite element simulation of interactions between pelvic organs: Predictive model of the prostate motion in the context of radiotherapy, J. Biomech., vol. 42, pp. 1862-1868, 2009. Other conventional registration methods calculate a medial axis between the fixed and moving images, and displace the FEM nodes based on an alignment of the medial axes. Crouch et al., Automated finite-element analysis for deformable registration of prostate images, IEEE TMI, vol. 26, no. 10, pp. 1379-1391, October 2007. The displacements are used as boundary conditions, and the FEM is used to calculate the displacement of the entire gland.
Conventional methods employ the alignment of the femoral heads for an initial rigid registration, after which the displacements between nodes on the organ surface are used as boundary conditions. For example, Hensel et al. used a FEM to register MR imagery acquired with an endorectal coil to MR imagery acquired without the endorectal coil. Hensel et al., Development of multiorgan finite element-based prostate deformation model enabling registration of endorectal coil magnetic resonance imaging for radiotherapy planning, Int. J. of Rad. Onc. Bio. Phys., vol. 68, no. 5, pp. 1522-1528, 2007. Conventionally, MR image to MR image registration involved calculating nodes on the surface of the prostate. The nodes are used as boundary conditions for an FEM that calculates deformations and forces. Brock et al., Accuracy and sensitivity of finite element model-based deformable registration of the prostate, Med. Phys., vol. 35, no. 9, pp. 4019-4025, September 2008.
Conventional FEM-based registration frameworks align nodes of one surface onto the nodes of another surface, typically using the Iterative Closest Points (ICP) algorithm. However, conventional methods assume that the node correspondences can be accurately determined. Furthermore, conventional FEM-based registration methods require the surfaces to be aligned, with no consideration of the imaging information. Conventional FEMs tend to focus on how external forces affect the surfaces and assume that the gland is a volume-preserving entity. Conventional methods therefore have sub-optimal accuracy when assessing early EBRT effectiveness, and when determining if early intervention in case of incomplete disease response to the EBRT is required.